A nonlinear energetic particle diffusion model with a variable source
- We investigate analytically and numerically the effect of a time-dependent source in a nonlinear model of diffusive particle transport, based on the p-Laplacian equation. The equation has been used to explain the observed cosmic-ray distributions and it appears in fluid dynamics and other areas of applied mathematics. We derive self-similar solutions for a class of the particle source functions and develop approximate analytical solutions, based on an integral method. We also use the fundamental solution to obtain an asymptotic description of an evolving particle density profile, and we use numerical simulations to investigate the accuracy of the analytical approximations.
| Author: | Yuri LitvinenkoORCiDGND, Dominik WalterGND, Horst FichtnerORCiDGND |
|---|---|
| URN: | urn:nbn:de:hbz:294-72529 |
| DOI: | https://doi.org/10.1063/1.5090953 |
| Parent Title (English): | AIP Advances |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2020/06/25 |
| Date of first Publication: | 2019/05/07 |
| Publishing Institution: | Ruhr-Universität Bochum, Universitätsbibliothek |
| Tag: | Open Access Fonds |
| Volume: | 9 |
| Issue: | 5, Artikel 055005 |
| First Page: | 055005-1 |
| Last Page: | 055005-11 |
| Note: | Article Processing Charge funded by the Deutsche Forschungsgemeinschaft (DFG) and the Open Access Publication Fund of Ruhr-Universität Bochum. |
| Institutes/Facilities: | Institut für Theoretische Physik IV |
| Dewey Decimal Classification: | Naturwissenschaften und Mathematik / Physik |
| open_access (DINI-Set): | open_access |
| Licence (English): |  Creative Commons - CC BY 4.0 - Attribution 4.0 International |
